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Mrs Merton once opened her eponymous satirical chat show by asking magician's wife Debbie McGee: "So, what first attracted you to the millionaire Paul Daniels?"

It is sometimes tempting to ask UK vice-chancellors the same question about international students, who in 2010-11 accounted for a 10th of the sector's total income. But with public funding being slashed and universities expected to make up the shortfall through tuition fees, there is little sense in berating them for protecting their bottom lines.

In any case, to focus solely on brass tacks would be a mistake since there are a multitude of reasons to accept students from across the world: cultural, social, intellectual and, yes, financial, although it is the national economy - not just the academy's - that benefits.

In our cover story this week, Edward Acton, vice-chancellor of the University of East Anglia, argues that the world-leading status of UK higher education has been built on foundations of "openness to international currents, cultures and collaboration".

In addition to their financial contribution, students from outside the European Union are propping up key disciplines at the postgraduate level, particularly in the science, technology, engineering and mathematics fields so valued by politicians and industry.

There are also "soft power" benefits, which, although harder to pin down, should not be underestimated: at one recent conference, for example, it was suggested that India's decision to award a £7 billion jet fighter contract to France rather than the UK was due in part to the latter's increasingly unfriendly student-visa regime.

All this suggests that a sensible approach to students within wider immigration policy matters not just to universities but also to the UK's economy, social and cultural life, and the industrial giants that politicians are normally so keen to court. Why, then, is the government continuing to endanger the flow of overseas students? The answer is politics, pure and simple: the Conservative manifesto pledged to cut net migration from hundreds of thousands to tens of thousands, and the Home Office is set on achieving this by hook or by crook.

But voters who want to see immigration cut (and many do) will not be won over at the ballot box by news that the number of fee-paying students has been slashed.

While there have been important concessions to lessen the visa crackdown's impact on universities, Acton argues that damage continues to be done. The offence is deepest, he says, where Anglophile feeling was once strong - a major problem when that includes India, soon to become the most populous country on Earth and with an ever-expanding middle class with cash to spend on education.

The solution proposed - that university-sponsored students be removed from the UK's net migration figures - is sensible and offers David Cameron a get-out clause that would help the coalition to hit its targets, too. But the Home Office insists that "fiddling the statistics" would not "restore public confidence".

Journalists are usually keen to pounce on any statistical jiggery-pokery, but such intransigence here seems misplaced. What is needed is cross-party agreement that university-sponsored students are an unalloyed good and should not figure in the often fevered immigration debate. Universities are united on this: politicians should be, too.